Cushioning dunnage is used as a protective packaging material when shipping an item in a container. The dunnage fills any voids and/or cushions the item in the container during shipping. Typical materials for forming cushioning dunnage include paper and plastic. Relatively complicated machines and methods are known for producing cushioning dunnage comprising resilient pillow-like strips from rolls of stock material. One such known machine is disclosed in U.S. Pat. No. 5,785,639. The known machines are disadvantageous in that they are suitable primarily for larger-scale productions and they are relatively expensive. There has long been a need in the packaging industry for a small and inexpensive device that creates and dispenses paper or other material for use as void fill and cushioning when shipping products in boxes or other containers.